Question

Suppose that $3$ is a factor of $a$, $a$ is a divisor of $12$, and $a$ is positive. What is the number of possible values of $a$

Answer 1

If $a$ is a divisor of 12, then

$a \in \{-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12\}$

If 3 is a factor (i.e. divisor) of $a$, then $a$ can only be one of the elements of this set that are multiples of 3, so

$a \in \{-12, -6, -3, 3, 6, 12\}$

But $a$ is positive, so there are 3 possible values $a$ can have.